Tim Seo: An Introduction to Abstract Harmonic Analysis
Time: Thu 2021-08-26 12.00 - 13.00
Respondent: Tim Seo
Abstract: This thesis will provide an introduction to Fourier analysis on locally compact abelian Hausdorff groups. The abstract Fourier transform unifies the classical Fourier transforms and will enable us not only to see the classical transforms as realizations in different groups but also lets us prove theorems regarding all of them in one stroke. The theory also gives us the opportunity to apply Fourier analysis in more exotic settings. Examples of Fourier Transforms are among many others the Fourier transform on the real line, Fourier series and the discrete Fourier transform. In the end two applications in number theory will be given.